Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E

Percentage Accurate: 92.9% → 97.3%

Time: 9.9s

Alternatives: 13

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / a)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Initial Program: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / a);
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / a)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{a} \cdot \left(z - t\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (/ y a) (- z t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y / a) * (z - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y / a) * (z - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y / a) * (z - t));
}

Python

def code(x, y, z, t, a):
	return x + ((y / a) * (z - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y / a) * Float64(z - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y / a) * (z - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.0%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
2. Step-by-step derivation

   1. associate-*l/ 97.3%

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

3. Simplified 97.3%

   \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

4. Final simplification 97.3%

   \[\leadsto x + \frac{y}{a} \cdot \left(z - t\right) \]

Alternative 2: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot z\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) z)))
   (if (<= a -5.2e+24)
     x
     (if (<= a -2.9e-137)
       t_1
       (if (<= a -1.2e-227)
         x
         (if (<= a -4.4e-271) (* y (/ z a)) (if (<= a 3.1e-65) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (a <= -5.2e+24) {
		tmp = x;
	} else if (a <= -2.9e-137) {
		tmp = t_1;
	} else if (a <= -1.2e-227) {
		tmp = x;
	} else if (a <= -4.4e-271) {
		tmp = y * (z / a);
	} else if (a <= 3.1e-65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * z
    if (a <= (-5.2d+24)) then
        tmp = x
    else if (a <= (-2.9d-137)) then
        tmp = t_1
    else if (a <= (-1.2d-227)) then
        tmp = x
    else if (a <= (-4.4d-271)) then
        tmp = y * (z / a)
    else if (a <= 3.1d-65) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (a <= -5.2e+24) {
		tmp = x;
	} else if (a <= -2.9e-137) {
		tmp = t_1;
	} else if (a <= -1.2e-227) {
		tmp = x;
	} else if (a <= -4.4e-271) {
		tmp = y * (z / a);
	} else if (a <= 3.1e-65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * z
	tmp = 0
	if a <= -5.2e+24:
		tmp = x
	elif a <= -2.9e-137:
		tmp = t_1
	elif a <= -1.2e-227:
		tmp = x
	elif a <= -4.4e-271:
		tmp = y * (z / a)
	elif a <= 3.1e-65:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (a <= -5.2e+24)
		tmp = x;
	elseif (a <= -2.9e-137)
		tmp = t_1;
	elseif (a <= -1.2e-227)
		tmp = x;
	elseif (a <= -4.4e-271)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= 3.1e-65)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * z;
	tmp = 0.0;
	if (a <= -5.2e+24)
		tmp = x;
	elseif (a <= -2.9e-137)
		tmp = t_1;
	elseif (a <= -1.2e-227)
		tmp = x;
	elseif (a <= -4.4e-271)
		tmp = y * (z / a);
	elseif (a <= 3.1e-65)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[a, -5.2e+24], x, If[LessEqual[a, -2.9e-137], t$95$1, If[LessEqual[a, -1.2e-227], x, If[LessEqual[a, -4.4e-271], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-65], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.1999999999999997e24 or -2.89999999999999985e-137 < a < -1.2e-227 or 3.10000000000000016e-65 < a

   1. Initial program 88.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.6%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 58.5%

      \[\leadsto \color{blue}{x} \]

   if -5.1999999999999997e24 < a < -2.89999999999999985e-137 or -4.3999999999999999e-271 < a < 3.10000000000000016e-65

   1. Initial program 98.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around inf 50.8%

      \[\leadsto \color{blue}{\frac{z}{a}} \cdot y \]
   6. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

      2. clear-num 50.7%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 50.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   7. Applied egg-rr 50.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 55.1%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   9. Applied egg-rr 55.1%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   if -1.2e-227 < a < -4.3999999999999999e-271

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.5%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 64.5%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around inf 79.1%

      \[\leadsto \color{blue}{\frac{z}{a}} \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-137}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot z\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) z)))
   (if (<= a -9.5e+26)
     x
     (if (<= a -5.2e-138)
       t_1
       (if (<= a -1.65e-227)
         x
         (if (<= a -6.5e-271) (/ y (/ a z)) (if (<= a 3.1e-64) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (a <= -9.5e+26) {
		tmp = x;
	} else if (a <= -5.2e-138) {
		tmp = t_1;
	} else if (a <= -1.65e-227) {
		tmp = x;
	} else if (a <= -6.5e-271) {
		tmp = y / (a / z);
	} else if (a <= 3.1e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * z
    if (a <= (-9.5d+26)) then
        tmp = x
    else if (a <= (-5.2d-138)) then
        tmp = t_1
    else if (a <= (-1.65d-227)) then
        tmp = x
    else if (a <= (-6.5d-271)) then
        tmp = y / (a / z)
    else if (a <= 3.1d-64) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (a <= -9.5e+26) {
		tmp = x;
	} else if (a <= -5.2e-138) {
		tmp = t_1;
	} else if (a <= -1.65e-227) {
		tmp = x;
	} else if (a <= -6.5e-271) {
		tmp = y / (a / z);
	} else if (a <= 3.1e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * z
	tmp = 0
	if a <= -9.5e+26:
		tmp = x
	elif a <= -5.2e-138:
		tmp = t_1
	elif a <= -1.65e-227:
		tmp = x
	elif a <= -6.5e-271:
		tmp = y / (a / z)
	elif a <= 3.1e-64:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (a <= -9.5e+26)
		tmp = x;
	elseif (a <= -5.2e-138)
		tmp = t_1;
	elseif (a <= -1.65e-227)
		tmp = x;
	elseif (a <= -6.5e-271)
		tmp = Float64(y / Float64(a / z));
	elseif (a <= 3.1e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * z;
	tmp = 0.0;
	if (a <= -9.5e+26)
		tmp = x;
	elseif (a <= -5.2e-138)
		tmp = t_1;
	elseif (a <= -1.65e-227)
		tmp = x;
	elseif (a <= -6.5e-271)
		tmp = y / (a / z);
	elseif (a <= 3.1e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[a, -9.5e+26], x, If[LessEqual[a, -5.2e-138], t$95$1, If[LessEqual[a, -1.65e-227], x, If[LessEqual[a, -6.5e-271], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-64], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.50000000000000054e26 or -5.2e-138 < a < -1.65e-227 or 3.10000000000000025e-64 < a

   1. Initial program 88.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.6%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 58.5%

      \[\leadsto \color{blue}{x} \]

   if -9.50000000000000054e26 < a < -5.2e-138 or -6.5000000000000005e-271 < a < 3.10000000000000025e-64

   1. Initial program 98.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 75.7%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around inf 50.8%

      \[\leadsto \color{blue}{\frac{z}{a}} \cdot y \]
   6. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

      2. clear-num 50.7%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 50.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   7. Applied egg-rr 50.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 55.1%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   9. Applied egg-rr 55.1%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   if -1.65e-227 < a < -6.5000000000000005e-271

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.5%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 64.5%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around inf 79.1%

      \[\leadsto \color{blue}{\frac{z}{a}} \cdot y \]
   6. Step-by-step derivation

      1. *-commutative 79.1%

         \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

      2. clear-num 79.1%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 80.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   7. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ t_2 := y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)) (t_2 (* y (- (/ t a)))))
   (if (<= a -6e+59)
     x
     (if (<= a -1.15e-225)
       t_2
       (if (<= a 1.1e-284)
         t_1
         (if (<= a 4.8e-217) t_2 (if (<= a 2.9e-65) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = y * -(t / a);
	double tmp;
	if (a <= -6e+59) {
		tmp = x;
	} else if (a <= -1.15e-225) {
		tmp = t_2;
	} else if (a <= 1.1e-284) {
		tmp = t_1;
	} else if (a <= 4.8e-217) {
		tmp = t_2;
	} else if (a <= 2.9e-65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / a
    t_2 = y * -(t / a)
    if (a <= (-6d+59)) then
        tmp = x
    else if (a <= (-1.15d-225)) then
        tmp = t_2
    else if (a <= 1.1d-284) then
        tmp = t_1
    else if (a <= 4.8d-217) then
        tmp = t_2
    else if (a <= 2.9d-65) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = y * -(t / a);
	double tmp;
	if (a <= -6e+59) {
		tmp = x;
	} else if (a <= -1.15e-225) {
		tmp = t_2;
	} else if (a <= 1.1e-284) {
		tmp = t_1;
	} else if (a <= 4.8e-217) {
		tmp = t_2;
	} else if (a <= 2.9e-65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	t_2 = y * -(t / a)
	tmp = 0
	if a <= -6e+59:
		tmp = x
	elif a <= -1.15e-225:
		tmp = t_2
	elif a <= 1.1e-284:
		tmp = t_1
	elif a <= 4.8e-217:
		tmp = t_2
	elif a <= 2.9e-65:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	t_2 = Float64(y * Float64(-Float64(t / a)))
	tmp = 0.0
	if (a <= -6e+59)
		tmp = x;
	elseif (a <= -1.15e-225)
		tmp = t_2;
	elseif (a <= 1.1e-284)
		tmp = t_1;
	elseif (a <= 4.8e-217)
		tmp = t_2;
	elseif (a <= 2.9e-65)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	t_2 = y * -(t / a);
	tmp = 0.0;
	if (a <= -6e+59)
		tmp = x;
	elseif (a <= -1.15e-225)
		tmp = t_2;
	elseif (a <= 1.1e-284)
		tmp = t_1;
	elseif (a <= 4.8e-217)
		tmp = t_2;
	elseif (a <= 2.9e-65)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[a, -6e+59], x, If[LessEqual[a, -1.15e-225], t$95$2, If[LessEqual[a, 1.1e-284], t$95$1, If[LessEqual[a, 4.8e-217], t$95$2, If[LessEqual[a, 2.9e-65], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.0000000000000001e59 or 2.8999999999999998e-65 < a

   1. Initial program 86.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x} \]

   if -6.0000000000000001e59 < a < -1.1499999999999999e-225 or 1.1e-284 < a < 4.7999999999999997e-217

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.3%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 71.4%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. associate-*r/ 51.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{a}} \cdot y \]

      2. neg-mul-1 51.4%

         \[\leadsto \frac{\color{blue}{-t}}{a} \cdot y \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\frac{-t}{a}} \cdot y \]

   if -1.1499999999999999e-225 < a < 1.1e-284 or 4.7999999999999997e-217 < a < 2.8999999999999998e-65

   1. Initial program 97.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.9%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 76.5%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 76.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 76.5%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 76.5%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto \color{blue}{\frac{\left(z - t\right) \cdot y}{a}} \]

      2. associate-/l* 76.9%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   9. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   10. Taylor expanded in z around inf 66.2%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-284}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ t_2 := \frac{t}{\frac{-a}{y}}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)) (t_2 (/ t (/ (- a) y))))
   (if (<= a -9.8e+55)
     x
     (if (<= a -2.3e-227)
       t_2
       (if (<= a 5.1e-287)
         t_1
         (if (<= a 5.4e-217) t_2 (if (<= a 2.95e-64) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = t / (-a / y);
	double tmp;
	if (a <= -9.8e+55) {
		tmp = x;
	} else if (a <= -2.3e-227) {
		tmp = t_2;
	} else if (a <= 5.1e-287) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 2.95e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / a
    t_2 = t / (-a / y)
    if (a <= (-9.8d+55)) then
        tmp = x
    else if (a <= (-2.3d-227)) then
        tmp = t_2
    else if (a <= 5.1d-287) then
        tmp = t_1
    else if (a <= 5.4d-217) then
        tmp = t_2
    else if (a <= 2.95d-64) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = t / (-a / y);
	double tmp;
	if (a <= -9.8e+55) {
		tmp = x;
	} else if (a <= -2.3e-227) {
		tmp = t_2;
	} else if (a <= 5.1e-287) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 2.95e-64) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	t_2 = t / (-a / y)
	tmp = 0
	if a <= -9.8e+55:
		tmp = x
	elif a <= -2.3e-227:
		tmp = t_2
	elif a <= 5.1e-287:
		tmp = t_1
	elif a <= 5.4e-217:
		tmp = t_2
	elif a <= 2.95e-64:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	t_2 = Float64(t / Float64(Float64(-a) / y))
	tmp = 0.0
	if (a <= -9.8e+55)
		tmp = x;
	elseif (a <= -2.3e-227)
		tmp = t_2;
	elseif (a <= 5.1e-287)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 2.95e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	t_2 = t / (-a / y);
	tmp = 0.0;
	if (a <= -9.8e+55)
		tmp = x;
	elseif (a <= -2.3e-227)
		tmp = t_2;
	elseif (a <= 5.1e-287)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 2.95e-64)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[((-a) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+55], x, If[LessEqual[a, -2.3e-227], t$95$2, If[LessEqual[a, 5.1e-287], t$95$1, If[LessEqual[a, 5.4e-217], t$95$2, If[LessEqual[a, 2.95e-64], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.80000000000000029e55 or 2.94999999999999997e-64 < a

   1. Initial program 86.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x} \]

   if -9.80000000000000029e55 < a < -2.30000000000000012e-227 or 5.0999999999999998e-287 < a < 5.40000000000000032e-217

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.3%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 71.4%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. associate-*r/ 51.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{a}} \cdot y \]

      2. neg-mul-1 51.4%

         \[\leadsto \frac{\color{blue}{-t}}{a} \cdot y \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\frac{-t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. associate-*l/ 59.4%

         \[\leadsto \color{blue}{\frac{\left(-t\right) \cdot y}{a}} \]

      2. add-cube-cbrt 58.8%

         \[\leadsto \frac{\left(-t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      3. times-frac 55.7%

         \[\leadsto \color{blue}{\frac{-t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}}} \]

      4. add-sqr-sqrt 26.7%

         \[\leadsto \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      5. sqrt-unprod 26.0%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      6. sqr-neg 26.0%

         \[\leadsto \frac{\sqrt{\color{blue}{t \cdot t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      7. sqrt-unprod 2.8%

         \[\leadsto \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      8. add-sqr-sqrt 3.6%

         \[\leadsto \frac{\color{blue}{t}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      9. times-frac 3.6%

         \[\leadsto \color{blue}{\frac{t \cdot y}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      10. *-commutative 3.6%

          \[\leadsto \frac{\color{blue}{y \cdot t}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}} \]

      11. add-cube-cbrt 3.6%

          \[\leadsto \frac{y \cdot t}{\color{blue}{a}} \]

      12. div-inv 3.6%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \frac{1}{a}} \]

      13. *-commutative 3.6%

          \[\leadsto \color{blue}{\left(t \cdot y\right)} \cdot \frac{1}{a} \]

      14. associate-*l* 3.6%

          \[\leadsto \color{blue}{t \cdot \left(y \cdot \frac{1}{a}\right)} \]

      15. div-inv 3.6%

          \[\leadsto t \cdot \color{blue}{\frac{y}{a}} \]

      16. clear-num 3.6%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      17. div-inv 3.6%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

      18. frac-2neg 3.6%

          \[\leadsto \color{blue}{\frac{-t}{-\frac{a}{y}}} \]

      19. add-sqr-sqrt 0.8%

          \[\leadsto \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{-\frac{a}{y}} \]

      20. sqrt-unprod 22.0%

          \[\leadsto \frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{-\frac{a}{y}} \]

      21. sqr-neg 22.0%

          \[\leadsto \frac{\sqrt{\color{blue}{t \cdot t}}}{-\frac{a}{y}} \]

      22. sqrt-unprod 29.3%

          \[\leadsto \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{-\frac{a}{y}} \]

      23. add-sqr-sqrt 57.8%

          \[\leadsto \frac{\color{blue}{t}}{-\frac{a}{y}} \]

      24. distribute-neg-frac 57.8%

          \[\leadsto \frac{t}{\color{blue}{\frac{-a}{y}}} \]

   9. Applied egg-rr 57.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{-a}{y}}} \]

   if -2.30000000000000012e-227 < a < 5.0999999999999998e-287 or 5.40000000000000032e-217 < a < 2.94999999999999997e-64

   1. Initial program 97.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.9%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 76.5%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 76.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 76.5%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 76.5%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto \color{blue}{\frac{\left(z - t\right) \cdot y}{a}} \]

      2. associate-/l* 76.9%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   9. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   10. Taylor expanded in z around inf 66.2%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-287}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-64}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ t_2 := \frac{y \cdot t}{-a}\\ \mathbf{if}\;a \leq -3 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)) (t_2 (/ (* y t) (- a))))
   (if (<= a -3e+55)
     x
     (if (<= a -1.05e-226)
       t_2
       (if (<= a 6.6e-286)
         t_1
         (if (<= a 5.4e-217) t_2 (if (<= a 7.2e-66) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = (y * t) / -a;
	double tmp;
	if (a <= -3e+55) {
		tmp = x;
	} else if (a <= -1.05e-226) {
		tmp = t_2;
	} else if (a <= 6.6e-286) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 7.2e-66) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / a
    t_2 = (y * t) / -a
    if (a <= (-3d+55)) then
        tmp = x
    else if (a <= (-1.05d-226)) then
        tmp = t_2
    else if (a <= 6.6d-286) then
        tmp = t_1
    else if (a <= 5.4d-217) then
        tmp = t_2
    else if (a <= 7.2d-66) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double t_2 = (y * t) / -a;
	double tmp;
	if (a <= -3e+55) {
		tmp = x;
	} else if (a <= -1.05e-226) {
		tmp = t_2;
	} else if (a <= 6.6e-286) {
		tmp = t_1;
	} else if (a <= 5.4e-217) {
		tmp = t_2;
	} else if (a <= 7.2e-66) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	t_2 = (y * t) / -a
	tmp = 0
	if a <= -3e+55:
		tmp = x
	elif a <= -1.05e-226:
		tmp = t_2
	elif a <= 6.6e-286:
		tmp = t_1
	elif a <= 5.4e-217:
		tmp = t_2
	elif a <= 7.2e-66:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	t_2 = Float64(Float64(y * t) / Float64(-a))
	tmp = 0.0
	if (a <= -3e+55)
		tmp = x;
	elseif (a <= -1.05e-226)
		tmp = t_2;
	elseif (a <= 6.6e-286)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 7.2e-66)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	t_2 = (y * t) / -a;
	tmp = 0.0;
	if (a <= -3e+55)
		tmp = x;
	elseif (a <= -1.05e-226)
		tmp = t_2;
	elseif (a <= 6.6e-286)
		tmp = t_1;
	elseif (a <= 5.4e-217)
		tmp = t_2;
	elseif (a <= 7.2e-66)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[a, -3e+55], x, If[LessEqual[a, -1.05e-226], t$95$2, If[LessEqual[a, 6.6e-286], t$95$1, If[LessEqual[a, 5.4e-217], t$95$2, If[LessEqual[a, 7.2e-66], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.00000000000000017e55 or 7.20000000000000025e-66 < a

   1. Initial program 86.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x} \]

   if -3.00000000000000017e55 < a < -1.0500000000000001e-226 or 6.5999999999999997e-286 < a < 5.40000000000000032e-217

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.3%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 71.4%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. associate-*r/ 51.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{a}} \cdot y \]

      2. neg-mul-1 51.4%

         \[\leadsto \frac{\color{blue}{-t}}{a} \cdot y \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{\frac{-t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \color{blue}{y \cdot \frac{-t}{a}} \]

      2. frac-2neg 51.4%

         \[\leadsto y \cdot \color{blue}{\frac{-\left(-t\right)}{-a}} \]

      3. remove-double-neg 51.4%

         \[\leadsto y \cdot \frac{\color{blue}{t}}{-a} \]

      4. associate-*r/ 59.4%

         \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

   9. Applied egg-rr 59.4%

      \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

   if -1.0500000000000001e-226 < a < 6.5999999999999997e-286 or 5.40000000000000032e-217 < a < 7.20000000000000025e-66

   1. Initial program 97.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.9%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 76.5%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 76.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 76.5%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 76.5%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 76.5%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. associate-*l/ 83.1%

         \[\leadsto \color{blue}{\frac{\left(z - t\right) \cdot y}{a}} \]

      2. associate-/l* 76.9%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   9. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\frac{z - t}{\frac{a}{y}}} \]

   10. Taylor expanded in z around inf 66.2%

       \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-226}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-286}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-217}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot z\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) z))))
   (if (<= x -6.4e-80)
     t_1
     (if (<= x 2.6e-6)
       (* y (/ (- z t) a))
       (if (<= x 8e+26)
         (+ x (/ y (/ a z)))
         (if (<= x 1.2e+37) (/ t (/ (- a) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * z);
	double tmp;
	if (x <= -6.4e-80) {
		tmp = t_1;
	} else if (x <= 2.6e-6) {
		tmp = y * ((z - t) / a);
	} else if (x <= 8e+26) {
		tmp = x + (y / (a / z));
	} else if (x <= 1.2e+37) {
		tmp = t / (-a / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / a) * z)
    if (x <= (-6.4d-80)) then
        tmp = t_1
    else if (x <= 2.6d-6) then
        tmp = y * ((z - t) / a)
    else if (x <= 8d+26) then
        tmp = x + (y / (a / z))
    else if (x <= 1.2d+37) then
        tmp = t / (-a / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * z);
	double tmp;
	if (x <= -6.4e-80) {
		tmp = t_1;
	} else if (x <= 2.6e-6) {
		tmp = y * ((z - t) / a);
	} else if (x <= 8e+26) {
		tmp = x + (y / (a / z));
	} else if (x <= 1.2e+37) {
		tmp = t / (-a / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * z)
	tmp = 0
	if x <= -6.4e-80:
		tmp = t_1
	elif x <= 2.6e-6:
		tmp = y * ((z - t) / a)
	elif x <= 8e+26:
		tmp = x + (y / (a / z))
	elif x <= 1.2e+37:
		tmp = t / (-a / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * z))
	tmp = 0.0
	if (x <= -6.4e-80)
		tmp = t_1;
	elseif (x <= 2.6e-6)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (x <= 8e+26)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (x <= 1.2e+37)
		tmp = Float64(t / Float64(Float64(-a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * z);
	tmp = 0.0;
	if (x <= -6.4e-80)
		tmp = t_1;
	elseif (x <= 2.6e-6)
		tmp = y * ((z - t) / a);
	elseif (x <= 8e+26)
		tmp = x + (y / (a / z));
	elseif (x <= 1.2e+37)
		tmp = t / (-a / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e-80], t$95$1, If[LessEqual[x, 2.6e-6], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+26], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+37], N[(t / N[((-a) / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.3999999999999998e-80 or 1.2e37 < x

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around 0 80.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. associate-*l/ 83.7%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

      2. *-commutative 83.7%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} + x \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a} + x} \]

   if -6.3999999999999998e-80 < x < 2.60000000000000009e-6

   1. Initial program 90.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 80.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 80.1%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 80.1%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   if 2.60000000000000009e-6 < x < 8.00000000000000038e26

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]

   4. Taylor expanded in z around inf 100.0%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if 8.00000000000000038e26 < x < 1.2e37

   1. Initial program 99.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 99.2%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 99.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. associate-*r/ 99.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot t}{a}} \cdot y \]

      2. neg-mul-1 99.2%

         \[\leadsto \frac{\color{blue}{-t}}{a} \cdot y \]

   7. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{-t}{a}} \cdot y \]
   8. Step-by-step derivation

      1. associate-*l/ 99.2%

         \[\leadsto \color{blue}{\frac{\left(-t\right) \cdot y}{a}} \]

      2. add-cube-cbrt 98.0%

         \[\leadsto \frac{\left(-t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      3. times-frac 97.9%

         \[\leadsto \color{blue}{\frac{-t}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}}} \]

      4. add-sqr-sqrt 24.4%

         \[\leadsto \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      5. sqrt-unprod 24.7%

         \[\leadsto \frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      6. sqr-neg 24.7%

         \[\leadsto \frac{\sqrt{\color{blue}{t \cdot t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      7. sqrt-unprod 0.4%

         \[\leadsto \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      8. add-sqr-sqrt 0.5%

         \[\leadsto \frac{\color{blue}{t}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a}} \]

      9. times-frac 0.5%

         \[\leadsto \color{blue}{\frac{t \cdot y}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}} \]

      10. *-commutative 0.5%

          \[\leadsto \frac{\color{blue}{y \cdot t}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}} \]

      11. add-cube-cbrt 0.5%

          \[\leadsto \frac{y \cdot t}{\color{blue}{a}} \]

      12. div-inv 0.5%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \frac{1}{a}} \]

      13. *-commutative 0.5%

          \[\leadsto \color{blue}{\left(t \cdot y\right)} \cdot \frac{1}{a} \]

      14. associate-*l* 0.5%

          \[\leadsto \color{blue}{t \cdot \left(y \cdot \frac{1}{a}\right)} \]

      15. div-inv 0.5%

          \[\leadsto t \cdot \color{blue}{\frac{y}{a}} \]

      16. clear-num 0.5%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      17. div-inv 0.5%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

      18. frac-2neg 0.5%

          \[\leadsto \color{blue}{\frac{-t}{-\frac{a}{y}}} \]

      19. add-sqr-sqrt 0.1%

          \[\leadsto \frac{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}{-\frac{a}{y}} \]

      20. sqrt-unprod 51.5%

          \[\leadsto \frac{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}{-\frac{a}{y}} \]

      21. sqr-neg 51.5%

          \[\leadsto \frac{\sqrt{\color{blue}{t \cdot t}}}{-\frac{a}{y}} \]

      22. sqrt-unprod 74.2%

          \[\leadsto \frac{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}{-\frac{a}{y}} \]

      23. add-sqr-sqrt 99.6%

          \[\leadsto \frac{\color{blue}{t}}{-\frac{a}{y}} \]

      24. distribute-neg-frac 99.6%

          \[\leadsto \frac{t}{\color{blue}{\frac{-a}{y}}} \]

   9. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{t}{\frac{-a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{\frac{-a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 8: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-81} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.6e-81) (not (<= x 5.8e-10)))
   (+ x (/ y (/ a z)))
   (* y (/ (- z t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.6e-81) || !(x <= 5.8e-10)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.6d-81)) .or. (.not. (x <= 5.8d-10))) then
        tmp = x + (y / (a / z))
    else
        tmp = y * ((z - t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.6e-81) || !(x <= 5.8e-10)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.6e-81) or not (x <= 5.8e-10):
		tmp = x + (y / (a / z))
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.6e-81) || !(x <= 5.8e-10))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.6e-81) || ~((x <= 5.8e-10)))
		tmp = x + (y / (a / z));
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.6e-81], N[Not[LessEqual[x, 5.8e-10]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-81 or 5.79999999999999962e-10 < x

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]

   4. Taylor expanded in z around inf 78.7%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if -2.5999999999999999e-81 < x < 5.79999999999999962e-10

   1. Initial program 90.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 80.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 80.1%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 80.1%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-81} \lor \neg \left(x \leq 5.8 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 9: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-75} \lor \neg \left(t \leq 1.6 \cdot 10^{+87}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.7e-75) (not (<= t 1.6e+87)))
   (- x (* (/ y a) t))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e-75) || !(t <= 1.6e+87)) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.7d-75)) .or. (.not. (t <= 1.6d+87))) then
        tmp = x - ((y / a) * t)
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.7e-75) || !(t <= 1.6e+87)) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.7e-75) or not (t <= 1.6e+87):
		tmp = x - ((y / a) * t)
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.7e-75) || !(t <= 1.6e+87))
		tmp = Float64(x - Float64(Float64(y / a) * t));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.7e-75) || ~((t <= 1.6e+87)))
		tmp = x - ((y / a) * t);
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.7e-75], N[Not[LessEqual[t, 1.6e+87]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.70000000000000024e-75 or 1.6e87 < t

   1. Initial program 90.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around 0 85.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{a} + x} \]
   5. Step-by-step derivation

      1. mul-1-neg 85.2%

         \[\leadsto \color{blue}{\left(-\frac{y \cdot t}{a}\right)} + x \]

      2. associate-*l/ 91.5%

         \[\leadsto \left(-\color{blue}{\frac{y}{a} \cdot t}\right) + x \]

      3. distribute-rgt-neg-out 91.5%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} + x \]

      4. +-commutative 91.5%

         \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(-t\right)} \]

      5. *-commutative 91.5%

         \[\leadsto x + \color{blue}{\left(-t\right) \cdot \frac{y}{a}} \]

      6. distribute-lft-neg-out 91.5%

         \[\leadsto x + \color{blue}{\left(-t \cdot \frac{y}{a}\right)} \]

      7. unsub-neg 91.5%

         \[\leadsto \color{blue}{x - t \cdot \frac{y}{a}} \]

   6. Simplified 91.5%

      \[\leadsto \color{blue}{x - t \cdot \frac{y}{a}} \]

   if -3.70000000000000024e-75 < t < 1.6e87

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around 0 82.7%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. associate-*l/ 87.7%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

      2. *-commutative 87.7%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} + x \]

   6. Simplified 87.7%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-75} \lor \neg \left(t \leq 1.6 \cdot 10^{+87}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 10: 65.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+205}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.15e+205) x (if (<= x 1.6e+40) (* y (/ (- z t) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.15e+205) {
		tmp = x;
	} else if (x <= 1.6e+40) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-3.15d+205)) then
        tmp = x
    else if (x <= 1.6d+40) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.15e+205) {
		tmp = x;
	} else if (x <= 1.6e+40) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.15e+205:
		tmp = x
	elif x <= 1.6e+40:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.15e+205)
		tmp = x;
	elseif (x <= 1.6e+40)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -3.15e+205)
		tmp = x;
	elseif (x <= 1.6e+40)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.15e+205], x, If[LessEqual[x, 1.6e+40], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.15000000000000007e205 or 1.5999999999999999e40 < x

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 76.1%

      \[\leadsto \color{blue}{x} \]

   if -3.15000000000000007e205 < x < 1.5999999999999999e40

   1. Initial program 91.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.1%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 69.4%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 69.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 69.4%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 69.4%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 69.4%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 69.4%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 69.4%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+205}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.6e-80)
   (+ x (* (/ y a) z))
   (if (<= x 7.6e-9) (* y (/ (- z t) a)) (+ x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.6e-80) {
		tmp = x + ((y / a) * z);
	} else if (x <= 7.6e-9) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.6d-80)) then
        tmp = x + ((y / a) * z)
    else if (x <= 7.6d-9) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.6e-80) {
		tmp = x + ((y / a) * z);
	} else if (x <= 7.6e-9) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.6e-80:
		tmp = x + ((y / a) * z)
	elif x <= 7.6e-9:
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.6e-80)
		tmp = Float64(x + Float64(Float64(y / a) * z));
	elseif (x <= 7.6e-9)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.6e-80)
		tmp = x + ((y / a) * z);
	elseif (x <= 7.6e-9)
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.6e-80], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-9], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.59999999999999978e-80

   1. Initial program 92.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around 0 74.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. associate-*l/ 81.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

      2. *-commutative 81.4%

         \[\leadsto \color{blue}{z \cdot \frac{y}{a}} + x \]

   6. Simplified 81.4%

      \[\leadsto \color{blue}{z \cdot \frac{y}{a} + x} \]

   if -5.59999999999999978e-80 < x < 7.60000000000000023e-9

   1. Initial program 90.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 80.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{t}{a} + \frac{z}{a}\right)} \cdot y \]
   6. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} + -1 \cdot \frac{t}{a}\right)} \cdot y \]

      2. mul-1-neg 80.1%

         \[\leadsto \left(\frac{z}{a} + \color{blue}{\left(-\frac{t}{a}\right)}\right) \cdot y \]

      3. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)} \cdot y \]

      4. div-sub 80.1%

         \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{z - t}{a}} \cdot y \]

   if 7.60000000000000023e-9 < x

   1. Initial program 95.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.6%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.6%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around 0 82.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 12: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e+24) x (if (<= a 7.8e-66) (* (/ y a) z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+24) {
		tmp = x;
	} else if (a <= 7.8e-66) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.05d+24)) then
        tmp = x
    else if (a <= 7.8d-66) then
        tmp = (y / a) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e+24) {
		tmp = x;
	} else if (a <= 7.8e-66) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e+24:
		tmp = x
	elif a <= 7.8e-66:
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e+24)
		tmp = x;
	elseif (a <= 7.8e-66)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.05e+24)
		tmp = x;
	elseif (a <= 7.8e-66)
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e+24], x, If[LessEqual[a, 7.8e-66], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05e24 or 7.79999999999999965e-66 < a

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in x around inf 61.7%

      \[\leadsto \color{blue}{x} \]

   if -2.05e24 < a < 7.79999999999999965e-66

   1. Initial program 98.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 95.0%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right) \cdot y} \]

   5. Taylor expanded in z around inf 45.9%

      \[\leadsto \color{blue}{\frac{z}{a}} \cdot y \]
   6. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

      2. clear-num 45.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 46.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   7. Applied egg-rr 46.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 47.9%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   9. Applied egg-rr 47.9%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 39.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 92.0%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
2. Step-by-step derivation

   1. associate-*l/ 97.3%

      \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

3. Simplified 97.3%

   \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(z - t\right)} \]

4. Taylor expanded in x around inf 42.8%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 42.8%

   \[\leadsto x \]

Developer target: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))